Exploring dynamics of plant–herbivore interactions: bifurcation analysis and chaos control with Holling type-II functional response

• Published in: Journal of mathematical biology Vol. 88; no. 1; p. 8
• Main Authors: Shabbir, Muhammad Sajjad, Din, Qamar, De la Sen, Manuel, Gómez-Aguilar, J. F.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.01.2024; Springer Nature B.V
• Subjects: Animals; Applications of Mathematics; Applied mathematics; Bifurcation theory; Borers; Control methods; Equilibrium; Herbivores; Herbivory; Investigations; Mathematical and Computational Biology; Mathematical models; Mathematics; Mathematics and Statistics; Models, Biological; Partial differential equations; Plants; Qualitative analysis; R&D; Research & development; Stability analysis; Neimark–Sacker bifurcation; 39A30; Transcritical bifurcation; 92D25; Plant–herbivore interactions; 40A05; Chaos control; 92C50
• ISSN: 0303-6812; 1432-1416
• DOI: 10.1007/s00285-023-02020-5

In this study, we examine the plant–herbivore discrete model of apple twig borer and grape vine interaction, with a particular emphasis on the extended weak-predator response to Holling type-II response. We explore the dynamical and qualitative analysis of this model and investigate the conditions for stability and bifurcation. Our study demonstrates the presence of the Neimark–Sacker bifurcation at the interior equilibrium and the transcritical bifurcation at the trivial equilibrium, both of which have biological feasibility. To avoid unpredictable outcomes due to bifurcation, we employ chaos control methods. Furthermore, to support our theoretical and mathematical findings, we develop numerical simulation techniques with examples. In summary, our research enhances the comprehension of the dynamics pertaining to interactions between plants and herbivores in the context of discrete-time population models.